What is the difference between a puzzle and a real world problem? A puzzle is devised by someone, generally with the intent of making a pleasant experience for the solver. In contrast, a real world problem is not guaranteed to have a solution, not guaranteed to have a feasible path towards a solution, and is not guaranteed to be pleasant to solve.

Here is a simple math puzzle. Can you design two six-sided dice whose sum follows the same probability distribution as 2D6, but with different numbers (all positive integers) on their faces? Classic, totally possible.

Here’s a simple real world physics problem: Can you estimate Earth’s equatorial bulge from its rotation speed and gravity? I thought I could estimate this using geometrical considerations, but that gives the wrong answer. The correct solution must account for the gravitational field of the bulge itself, which can be calculated by decomposing it into spherical harmonics. Nobody wants to do that.

Puzzles do not always succeed at being enjoyable. Sometimes you waste a lot of time on a puzzle, and then when you look up the solution you think, “I was never going to get that one.” For example, one time I picked up a puzzle box on a friend’s shelf, despite my friend’s insistence that the puzzle was stupid. After messing around a bit, he showed me how to open it: he slammed it hard on the table to shake a magnet loose. I was never going to solve that one, because I happen to have reservations about slamming potentially delicate objects that do not belong to me.

Puzzles can fail for a variety of reasons. Sometimes there is a mismatch between the puzzle and the solver. If you aren’t good with probabilities, you may not enjoy the dice problem, that’s okay. I am not familiar with the conventions of cryptic crosswords, so throwing one at me is unfair.

And of course, maybe the puzzle designer just didn’t do a good job. Often puzzle designers work in isolation, and they don’t really know what the solving experience is like. They just follow some intuition about what feels good or clever. But there’s a fundamental difference in the what the designer knows and what the solver knows, so puzzle designer intuitions are frequently wrong. For example, red herrings often dominate the solving experience, while being completely invisible to the designer.

There are certain puzzle design values that can work against designers. For instance, if you value “think outside the box”, this can turn into an arms race of cleverness. Every puzzle must break expectations, do something totally new and different. Eventually the designer gets what they wanted, a solution that nobody would ever think of. And puzzle solvers respond, “I never would have thought of that solution.”  It turns out that solvers don’t like that, go figure.

There’s also the sort of puzzle that celebrates excessive difficulty. For example, consider the sort of puzzle that promotes a nation-wide puzzle hunt, offering a money prize to the first solver. This sort of thing used to be much more fashionable, see this video for an example from 1984. The solution involved picking Carl Sagan’s Cosmos, first edition, flipping to Chapter 6, and mapping each number to the first letter of the corresponding word, with some rules for dealing with hyphenated words, acronyms, etc. The appeal in this puzzle is the thrilling fantasy of being the first solver, however impossible that may be. But as a puzzle that’s just unfair.

Difficult puzzles requires some degree of trust. As a solver, I want some assurance that the time investment will pay off. I need to have some faith in the competence of the puzzle designer, some indication that they’re not trying to out-clever or out-difficult themselves.

Puzzle video games generally benefit from the norm that games should be playtested. At least someone tried these puzzles, and gave feedback to the designer. But even this is not perfect.

I play a lot of puzzle games. As a result, I tend to be good at them. I’m not the best, but I do alright with many of the hardest puzzle games. Nonetheless, I have relatively low trust as a solver. From my broad experience, I know there are lots of puzzles out there that aren’t very good, or at the very least don’t mesh with me. They’re not worth my time. I am not interested in gritting my teeth through a bad puzzle. I do not need to “up” my puzzle skill level; at this level, puzzle solving is not a useful real life skill. Puzzles are not so precious that I need to savor every single one.

In my opinion, less-experience puzzle gamers tend to be higher in trust. After all, being less-experienced means you’ve played relatively few puzzle games, typically the greatest hits. If you’re only playing the greatest hits, you have little reason to mistrust.

To illustrate my perspective, let’s consider what is sometimes called the most difficult video game puzzle of all time: The Fez Monolith puzzle. To solve the puzzle, you must be in a particular room and give an exact series of inputs. The series of inputs was discovered by brute force. Nobody knows how the inputs were intended to be discovered. A variety of theories have been proposed, but none are things that a player plausibly could have figured out from the beginning, without working backwards from the real answer.

The monolith puzzle commands a certain degree of reverence from players. But to me, that’s just a bad puzzle. This puzzle was designed with the intent of being very challenging, and was likely never playtested. It’s the modern equivalent of those puzzles from the 80s with money prizes. To the extent that people appreciate the monolith puzzle, they do not appreciate it as a puzzle, they appreciate it as a communal mystery.

Here’s another very difficult puzzle from a more obscure game. Hack ‘n’ Slash is a hacking puzzle game made by Double Fine in 2014. At first you hack objects using a clean gamey interface. But eventually you can navigate the game’s actual code, and that was something of a difficulty cliff. It also feels distinctly like the game was abandoned part way through its development. I played this game, and solved most of it, but there was one puzzle that required you to input a password. There was no getting around the password; the password was an encryption key for a file that was actually encrypted. Nobody knew how to solve the puzzle.

I found out when researching this, that someone finally solved the puzzle in 2022. The password was apparently a phrase that appeared in the loading screen. The solver used brute force, as well as a hint from the devs to narrow it down. Solving the puzzle gave you access to some dev commentary (although I’m afraid that a decade later, it’s all meaningless to me).

Was this a good puzzle? No. As an optional challenge, I suspect the designers did not meaningfully playtest the puzzle. When they picked a passphrase that appeared on the loading screen, I think they did not realize just how many equally likely passwords there would be from the solver perspective. It’s just a classic case of puzzle designers failing to respect the difference in knowledge between puzzle solvers and designers.

But, if you get good at solving bad puzzles, such a skill may have practical value. After all, the universe is one of the worst puzzle designers around.